# A real gas with gravitation-like interaction

Consider a system (a gas) of point-like particles with a gravitation-like interaction (potential) $V(r) \sim \frac{1}{r}$ between pairs of them.

One can rule out statistically that two particles will approach each other exactly along their line, so two particles will never collide directly - thus giving rise to infinite (kinetic) energies. So the particles will always whirl around each other in one way or the other.

What can be said about such a system in the framework of statistical mechanics?

How does its partition function look like?

What are its thermodynamical equilibrium states?

What happens when cooling such a system down (e.g. from very high temperatures)?

• I might be wrong, but wouldn't such a system be able to provide an infinite amount of energy upon cooling? – DumpsterDoofus Apr 1 '14 at 0:06
• @DumpsterDoofus: You probably are right - but that's the kind of objection I am looking for! (But maybe the system is all that there is - and it cannot be cooled "from the outside"?) – Hans-Peter Stricker Apr 1 '14 at 0:16
• I'm not sure exactly how to tackle this because I would have to consider interactions between every pair.. but why wouldn't they all be at r=0 in equilibrium? The Boltzmann factor for r=0 between all particles would be infinite for this configuration wouldn't it? – Julien Apr 1 '14 at 0:29
• I believe this is a major unsolved problem in cosmology, although I haven't looked into it in any depth. – Nathaniel Apr 1 '14 at 1:48
• I think at about $V^{1/3}= \frac{2V \rho G}{c^2}$ it would form a black hole. – Mirc Breitschuh Apr 1 '14 at 9:14